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MathLapse- L- System for Single Knot Kolam Pattern Generation

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BRUNDA ALAGARSAMY

In the art form of SUZHIKOLAM/ KAMBIKOLAM, dots called pulli are arranged in rhombic, square, triangular, or free shapes, and a single, uninterrupted linear or curvilinear line, called the kambi, intertwines the dots.
L-System
Lindermayer system is a parallel rewriting system and a type of formal grammar. It consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols.
The recursive nature of L system rules leads to self similarity and thereby fractal like forms are easy to describe with an L system. This nature is applied in generating kolam pattern. Kolam pattern becomes more complex by increasing the iteration level.
Software: Python Turtle Graphics

SUZHI / KAMBI / SIKKU KolamIn the art form of SUZHIKOLAM/ KAMBIKOLAM, dots called pulli are arranged inrhombic, square, triangular, or free shapes, and a single, uninterrupted linear or curvilinear line,called the kambi, intertwines the dots. While there are no written or verbally stated rules. Listedsome rules of pulli(dots) and kambi/Suzhi kolam from examining the designs (Yanagisawa,Nagata, Robinson Thamburaj). Rules can be added / removed.Rule 1: Uniformly spacing of dotsRule 2: Smooth drawing line around the dotsRule 3: Symmetry in drawingsRule 4: Straight lines are drawn inclined at an angle of 45 degreesRule 5: Drawing lines never trace backRule 6: Arcs adjoining the dotsRule 7 : Kolam is completed when all points are enclosed by the drawing lineKolam drawing can be treated as a special kind of a graph with the crossings consideredas vertices and the parts of the kambi between vertices treated as edges. The only restriction isthat unlike in a graph, these edges cannot be freely drawn as there is a specific way of drawingthe kolam. The single kambi kolam will then be an Eulerian graph with the drawing starting andending in the same vertex and passing through every edge of the graph only once. Single knotkolam also called as “ANTHATHI Kolam” in Tamil Nadu. The Smooth line starts at a point andend in the same point. Single knot kolam can be drawn for any type of dot structure (rhombic,square, triangular, or free shapes).L-SystemLindermayer system is a parallel rewriting system and a type of formal grammar. It consists ofan alphabet of symbols that can be used to make strings, a collection of production rules thatexpand each symbol into some larger string of symbols.The recursive nature of L system rules leads to self similarity and thereby fractal like forms areeasy to describe with an L system. This nature is applied in generating kolam pattern. Kolampattern becomes more complex by increasing the iteration level.Software: Python Turtle GraphicsApplying L-System for Kolam pattern Generation:Procedure:Axiom or Initiator: FBFBFBFBRules: A AFBFA B AFBFBFBFAAngle: 45oFrom current cursor position ,F Forward 10 units (draw a line 10 units length)A Draw an arc (circle (10, 90))B Calculate forward units I = 5/sqrt (2)Forward I UnitsDraw an arc (circle (I, 270))Forward I Units